BandaBeau Orders Forecast

library(forecast)
library(smooth)

BandaBeauOrdersTrain = BandaBeauOrdersGrouped[1:13,]
BandaBeauOrdersTest = BandaBeauOrdersGrouped[14:17,]

#Simple Moving Average
library(tseries)

    ‘tseries’ version: 0.10-45

    ‘tseries’ is a package for time series analysis and computational finance.

    See ‘library(help="tseries")’ for details.

library(greybox)
library(smooth)
SMAmodel = sma(BandaBeauOrdersTrain$`Order Count`, h = 4)
summary(SMAmodel)

Time elapsed: 0.01 seconds
Model estimated: SMA(2)
Initial values were produced using backcasting.
2 parameters were estimated in the process
Residuals standard deviation: 43.039
Cost function type: MSE; Cost function value: 1567.356

Information criteria:
     AIC     AICc      BIC     BICc 
136.5353 137.7353 137.6652 139.2042 

SMAmodel.predict = forecast(SMAmodel, h = 4)
plot(SMAmodel.predict)

#Check Accuracy
sqrt(mean((SMAmodel.predict$forecast - BandaBeauOrdersTest$`Order Count`)^2))

[1] 53.68911

MAPE(SMAmodel.predict$forecast, BandaBeauOrdersTest$`Order Count`)

[1] 0.551

#Fit Holt Winters Model
HoltWintersModel = HoltWinters(BandaBeauOrdersTrain$`Order Count`, alpha = 0.2, beta = F, gamma = F)
#Predict using Holt Wintes model
HoltWintersModel.predict = forecast(HoltWintersModel, n.ahead = 4, prediction.interval = T)
#Plot predictions
plot(HoltWintersModel.predict)

#plot.ts(BandaBeauOrdersTrain$`Order Count`, xlim = c(1, 17))
#lines(HoltWintersModel$fitted[,1], col = "blue")
#lines(HoltWintersModel.predict[,1], col = "red")

# Calculate RMSE
sqrt(mean(HoltWintersModel.predict[,1] - BandaBeauOrdersTest$`Order Count`)^2)

Error in HoltWintersModel.predict[, 1] : incorrect number of dimensions

#Calculate MAPE
MAPE(HoltWintersModel.predict[,1], BandaBeauOrdersTest$`Order Count`)

[1] 0.512

HoltWintersModel.predict$mean

Time Series:
Start = 14 
End = 23 
Frequency = 1 
 [1] 64.64748 64.64748 64.64748 64.64748 64.64748 64.64748 64.64748 64.64748 64.64748
[10] 64.64748

#ARIMA model
ArimaModel = auto.arima(BandaBeauOrdersTrain$`Order Count`, trace = T, ic = "aic")

 ARIMA(2,0,2) with non-zero mean : Inf
 ARIMA(0,0,0) with non-zero mean : 136.8095
 ARIMA(1,0,0) with non-zero mean : 137.3439
 ARIMA(0,0,1) with non-zero mean : 137.6662
 ARIMA(0,0,0) with zero mean     : 146.0816
 ARIMA(1,0,1) with non-zero mean : 139.1863

 Best model: ARIMA(0,0,0) with non-zero mean 

#ArimaModel = arima(BandaBeauOrdersTrain$`Order Count`, order = c(0,0,1))
summary(ArimaModel)

Series: BandaBeauOrdersTrain$`Order Count` 
ARIMA(0,0,0) with non-zero mean 

Coefficients:
         mean
      47.0000
s.e.  11.0967

sigma^2 estimated as 1734:  log likelihood=-66.4
AIC=136.81   AICc=138.01   BIC=137.94

Training set error measures:
                       ME     RMSE MAE     MPE    MAPE      MASE      ACF1
Training set 2.186179e-14 40.00961  34 -196.37 228.871 0.9422633 0.3022105

confint(ArimaModel)

             2.5 %   97.5 %
intercept 25.25083 68.74917

#Check ACF and PACF plots
acf(diff(BandaBeauOrdersTrain$`Order Count`))

#Check PACF plot
pacf(diff(BandaBeauOrdersTrain$`Order Count`))

ArimaModel.predict = forecast(ArimaModel, h = 4)
plot(ArimaModel.predict)

#Calculate accuracy
sqrt(mean((ArimaModel.predict$mean - BandaBeauOrdersTest$`Order Count`)^2))

[1] 25.36184

MAPE(ArimaModel.predict$mean, BandaBeauOrdersTest$`Order Count`)

[1] 0.481

summary(ArimaModel)

Call:
arima(x = BandaBeauOrdersTrain$`Order Count`, order = c(0, 0, 1))

Coefficients:
         ma1  intercept
      0.2885    48.4678
s.e.  0.2634    13.4326

sigma^2 estimated as 1456:  log likelihood = -65.83,  aic = 137.67

Training set error measures:
                     ME     RMSE      MAE       MPE     MAPE      MASE        ACF1
Training set -0.9614872 38.16056 33.20744 -174.8805 206.4537 0.9202987 0.008750646

#Selected ARIMA model to be the best
#ArimaModel2 = auto.arima(BandaBeauOrdersTrain$`Order Count`, trace = T, ic = "aic")
ArimaModel2 = arima(BandaBeauOrdersGrouped$`Order Count`, order = c(0,0,5))
summary(ArimaModel2)

Call:
arima(x = BandaBeauOrdersGrouped$`Order Count`, order = c(0, 0, 5))

Coefficients:
         ma1      ma2      ma3      ma4      ma5  intercept
      0.1889  -0.1064  -0.3614  -0.3903  -0.3308    46.8794
s.e.  0.3151   0.3250   0.2900   0.3366   0.2485     4.8386

sigma^2 estimated as 942.1:  log likelihood = -83.33,  aic = 180.67

Training set error measures:
                    ME     RMSE      MAE       MPE    MAPE      MASE        ACF1
Training set -2.722802 30.69442 25.79768 -131.2096 156.142 0.8271802 -0.07404934

#Forecast for next 6 months
ArimaModel2.predict = forecast(ArimaModel2, h = 6)

NewDates = seq(from = as.Date("2018/11/01"), to = as.Date("2019/04/01"), "months")
#AllDates = rbind(BandaBeauOrdersGrouped$Date, NewDates)
AllDates = c(BandaBeauOrdersGrouped$Date, NewDates)
AllOrders = c(BandaBeauOrdersGrouped$`Order Count`, ArimaModel2.predict$mean)
AllOrders = round(AllOrders,0)

f = list(
  family = "Courier New, monospace",
  size = 18,
  color = "#7f7f7f"
)
x = list(title = "Date", titlefont = f)
y = list(title = "Order Count", titlefont = f)
library(plotly)
fig <- plot_ly(x = AllDates, y = AllOrders, mode = "lines", type = "scatter", name = "Forecast", line = list(color = 'rgb(205, 12, 24)', width = 4)) %>% layout(xaxis = x, yaxis = y, title = "BandaBeau Orders") %>% add_trace(y = BandaBeauOrdersGrouped$`Order Count`, x = BandaBeauOrdersGrouped$Date, name = "Original" ,line = list(color = 'rgb(22, 96, 167)', width = 4))
fig